On preservation under homomorphisms and unions of conjunctive queries
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
On digraph coloring problems and treewidth duality
European Journal of Combinatorics
Homomorphism preservation theorems
Journal of the ACM (JACM)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
Universal algebra and hardness results for constraint satisfaction problems
Theoretical Computer Science
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Universal algebra and hardness results for constraint satisfaction problems
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Preservations theorems, which establish connection betweensyntactic and semantic properties of formulas, area major topic of investigation in model theory. In the contextof finite-model theory, most, but not all, preservationtheorems are known to fail. It is not known, however,whether the 拢os-Tarski-Lyndon Theorem, which assertsthat a 1st-order sentence is preserved under homomorphismsiff it is equivalent to an existential positive sentence,holds with respect to finite structures. Resolvingthis is an important open question in finite-model theory.In this paper we study the relationship between closureunder homomorphism and positive syntax for several non-1st-order existential logics that are of interest in computerscience. We prove that the 拢os-Tarski-Lyndon Theoremholds for these logics. The logics we consider arevariable-confined existential infinitary logic, Datalog, andvarious fragments of second-order logic.